What is the best neural network architecture for this problem?
I'm not completely sure I understand your simulation. What I think you are doing is:


Generate 5 angles specified in radians (Are these always normalized to within (0, $2*\pi$)?).
Interpret each angle as a unit vector in a 2d space.
Add the unit vectors together, yielding a vector that lies somewhere inside a circle with radius 5.
Ask whether the summed vector is more or less than a distance $y$ from the origin of the circle.


If you're doing that, your problem looks like trying to learn a separation of two concentric rings, which is a well known benchmarking problem for classification. 

I am reasonably certain you can learn this pattern with several layers of ReLU neurons. I'm not certain that convolutional layers will help you much here. The main patterns I'd expect the network to learn are:


perhaps 2-3 layers to learn whether the point lies far away from the origin in each of several different directions.
1 layer to learn where the decision boundary is in each of 4 directions away from the origin.
1 layer to inclusive-OR the 4 decision boundaries together.


My guess is that this is fairly easy to learn with 4 layers of 8 ReLU neurons, or something like it.